In order to remove aliasing, direct conversion transceivers, for example, require an analog low-pass filter (LPF) at a stage subsequent to a digital-analog converter (DAC) or at a stage previous to an analog-digital converter (ADC).
Transmission systems using millimeter-wave bands or broadband signals, such as UWB (Ultra Wide Band), have become more common in recent years, and therefore, demand has been raised for a large increase in the sampling rates of digital-analog converters and analog-digital converters.
For example, in the case where the baseband frequency is 600 MHz, a sampling rate of at least 1.2 GHz is required. Digital-analog converters and analog-digital converters having such sampling rates have already been in the marketplace; however, even when a 1.2 GHz digital-analog converter is used, aliasing occurs in the bandwidth between 600 and 1200 MHz. Therefore, unless aliasing in this bandwidth is removed by a low-pass filter, adjacent channel interference occurs. Similarly in the case of analog-digital converters, it is necessary to cut off adjacent channels in advance by a low-pass filter in order to prevent adjacent channel interference.
Low-pass filters used for this purpose need to have steep cut-off characteristics. Examples of common low-pass filters having steep cut-off characteristics are Chebyshev filters, inverse Chebyshev filters and elliptic filters. Although such a filter has a steep cut-off characteristic, phase linearity is lost particularly around the cutoff frequency, and the group delay characteristics are degraded.
In the case where the group delay characteristics of a filter are degraded, when an input waveform passes through the filter, an output waveform becomes distorted. As a result, significant degradation is observed in the transmission characteristics. Accordingly, methods for improving the group delay characteristics of low-pass filters have conventionally been studied.
One such method is to insert an equalizer in a transmitter to produce a preliminarily distorted output, thereby correcting the distortion caused when the input waveform passes through the low-pass filter (see Patent Documents 1 and 2, for example).
Another method suggests the use of an equalizer with such a filter that causes the group delay characteristics to have a concave shape in the middle of the spectral frequencies and have a convex shape at edges of the spectral frequencies (see Patent Document 3, for example).
Yet another method is to improve the group delay characteristics by devising the shape of an analog filter (see Patent Document 4, for example).    [Patent Document 1] Japanese Laid-open Patent Application Publication No. 2000-299652    [Patent Document 2] Japanese Laid-open Patent Application Publication No. 2001-257564    [Patent Document 3] Japanese Laid-open Patent Application Publication No. S62-227208    [Patent Document 4] Japanese Laid-open Patent Application Publication No. H11-261303
However, neither Patent Document 1 nor Patent Document 2 discloses a method for calculating the inverse characteristics of the group delay characteristics of the filter. The correction technique of Patent Document 3 is directed only to a filter whose group delay characteristics have a concave shape in the middle of the spectral frequencies and a convex shape at edges of the spectral frequencies.
The technique of Patent Document 4 requires a large cost since the analog filter itself is devised, and also leaves the problem of less design freedom in terms of the pass band, cutoff band and the like.